An analytical approach to codimension-2 sliding bifurcations in the dry friction oscillator

Abstract

In this paper, we analytically consider sliding bifurcations of periodic orbits in the dry-friction oscillator. The system depends on two parameters: F, which corresponds to the intensity of the friction, and ω, the frequency of the forcing. We prove the existence of infinitely many codimension-2 bifurcation points and focus our attention on two of them: A1 := (ω −1, F) = (2, 1/3) and B1 := (ω −1, F) = (3, 0). We derive analytic expressions in (ω −1, F) parameter space for the codimension-1 bifurcation curves that emanate from A1 and B1. Our results show excellent agreement with the numerical calculations of Kowalczyk and Piiroinen [Phys. D, 237 (2008), pp. 1053–1073].